What is the 378th prime number?
The 378th prime number is 2593. The next prime is 2609 (a gap of 16) and the one before is 2591.
Position
Pick any whole number from 1 to 10,000.
How to work it out
- 1
List the primes in order: 2, 3, 5, 7, 11, 13, ā¦ The 378th one is 2593.
- 2
2593 is prime because no prime up to ā2593 ā 50.92 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 378th prime is close to 378 Ć ln(378) ā 2243, and here it is 2593.
- 4
2593 is a twin prime: 2591 and 2593 are both prime.
Primes around the 378th
| Position | Prime | Gap from the previous |
|---|---|---|
| 375 | 2557 | 6 |
| 376 | 2579 | 22 |
| 377 | 2591 | 12 |
| 378 | 2593 | 2 |
| 379 | 2609 | 16 |
| 380 | 2617 | 8 |
| 381 | 2621 | 4 |
Questions
What is the 378th prime number?
2593.
Which prime number is 2593?
2593 is the 378th prime number.
What is the sum of the first 378 primes?
448,869.